🌐 Dimensions: From Geometry to Orders of Existence

A Foundational Page of Similarity Theory
By Simon Raphael

What if dimension describes not just the geometry of space — but the range of what a being can do, experience, and understand?

🤔Here's something most people have probably never thought to ask:

If we live in the third dimension... where are the first and second?

The usual answer from a textbook is straightforward. A line is one-dimensional, a flat plane is two-dimensional, and the world we live in is three-dimensional. Easy enough.

But here's where it gets interesting.

When we say we live in a three-dimensional world, we don't just mean coordinates. We mean we exist here. We move here. We bump into things, fall in love, build cities, cross oceans and look up at the stars. The third dimension isn't merely something we calculate. It is something we inhabit.

So why, when we ask where the first and second dimensions are, do our answers suddenly become purely geometric? We point to a line on paper, a flat plane in a mathematics textbook, or an abstract coordinate system — not something we would encounter in the garden or recognise as a world.

💡 When we look above our own dimension, we imagine other beings living there. When we look below, we see only geometry. Why the double standard?

What if the lower dimensions were never empty? What if they have been around us all along — and we simply haven't recognised them for what they are?

🔄 A New Way to Think About Dimension

In mathematics, each new dimension introduces an additional degree of freedom. A line allows something a single point cannot. A plane introduces possibilities unavailable to a line. Three-dimensional space opens directions that a flat surface does not possess.

But what if this same principle — the introduction of genuinely new freedoms — applies not only to geometry, but to existence itself?

What if dimension can describe not merely how many directions exist in space, but how many kinds of relationship a being can enter into with reality?

A new dimension, in this sense, does not simply add more of what was already there. It introduces something fundamentally new: a new way of participating and a new kind of freedom.

Under this lens, the familiar progression begins to look something like this:

✦ Existence → Life and Growth → Agency

And perhaps the story does not end there.

Let's begin at the bottom.

⚛️ The First Dimension — Simply Existing

At the most fundamental level, there are things that simply... are.

Stones, crystals, mountains, oceans, atoms and the Earth's atmosphere are not passive nothings. Matter is constantly interacting. Gravity pulls, chemistry transforms, pressure builds and releases, minerals form and dissolve, stars ignite and planets move. Everything participates in relationships of some kind.

But a stone does not appear to organise itself around biological survival. It does not grow roots toward water, reproduce itself as a living organism, or leave one environment and deliberately move into another.

It exists, interacts and changes. It enters into physical relationships with everything around it, but its range of participation is limited.

The first dimension of existence: to be, to interact, and to undergo and participate in physical change.

This is not nothing. It is the foundation upon which everything else depends.

🌱 The Second Dimension — Coming Alive

Then something extraordinary becomes possible: life.

A plant is still made of atoms and molecules. Everything belonging to the first dimension remains present. But something new is now being expressed through them.

The plant grows, maintains itself, repairs damage, reproduces and responds to light. Its roots grow through soil toward water and nutrients. Its entire biological organisation participates in maintaining the continuity of the living being.

This does not mean that consciousness suddenly appeared because matter became sufficiently complicated. Rather, something deeper has happened. Consciousness has entered into a richer order of relationship, and through that richer relational organisation, new possibilities become available: growth, self-maintenance, reproduction, adaptation and life.

The organisation does not create consciousness. Organisation is one of the ways consciousness expresses itself through increasingly complex relations.

But notice something important. The plant's freedom is still limited.

A plant can turn toward light through growth. It can react to damage. It can send chemical signals. Some plants can even respond in surprisingly sophisticated ways to their surroundings. But if the soil becomes poor, the plant cannot normally pull up its roots and walk somewhere else. If darkness falls across one side of the room, it cannot pack its bags and move beside the window.

Its relationship with reality is rich and dynamic — but largely anchored to where it already is.

The second dimension: Existence + Life and Growth — the capacity to maintain, develop and participate in one's own living continuity.

The first dimension has not disappeared. It is still there, but something has been added to it.

🐾 The Third Dimension — Taking the Wheel

Then another freedom appears: agency.

A bee navigates back to its hive. An ant finds food and communicates its discovery. A crow solves a problem to reach a reward. A wolf tracks prey across kilometres of terrain. A dog chooses whether to approach, retreat, explore or wait.

What has changed?

These beings do not merely respond from where they are. They can actively change their relationship to where they are. They move toward food and away from danger. They seek shelter, explore, learn, alter their behaviour and navigate reality.

The world has changed from something that primarily happens around the organism into something the organism can actively move through and act upon.

That is a profound new freedom.

Humans extend agency to an extraordinary degree. We do not merely navigate our environment; we transform it. We cross oceans, build cities, launch spacecraft, store memories outside our bodies, create languages, and imagine things that do not yet exist — then attempt to bring them into existence.

But all of this still grows from the same fundamental freedom: the ability to act in relation to the world, to choose a direction, pursue, avoid, explore and intervene.

The bee, the crow, the wolf and the human all participate in agency, although the range and depth of their relationships may differ enormously.

The pattern begins to emerge. Each new dimension does not merely give existence more of what it already possessed. It opens a new category of possibility.

Life is not simply matter that became extremely complicated, and agency is not merely life with better machinery. Each represents a new relational freedom.

So the stack looks like this:

• First Dimension: Existence

• Second Dimension: Existence + Life and Growth

• Third Dimension: Existence + Life + Agency

• Fourth Dimension: Existence + Life + Agency + ?

That final question will have to wait. For now.

📏 Wait — A Plant Isn't Literally Flat

Before you object: yes, a stone, a tree, an eagle and a person all occupy ordinary three-dimensional space. A plant is not geometrically two-dimensional, and a rock is not literally a line.

That is not the claim.

The word dimension is being used here in two different ways:

Geometric dimension asks how many independent spatial directions are available.

Relational dimension asks what kinds of freedom are available in a being's relationship with reality.

These are different questions. They may share an underlying pattern — each additional dimension introduces possibilities unavailable at the level below — but they are describing different aspects of existence.

Geometry asks: How many spatial directions are available? Relational dimension asks: What kinds of engagement with reality are available?

Once that distinction is made, something rather interesting happens.

The lower dimensions may not be missing at all.

They may simply be hiding in plain sight.

🧠 Complexity Is Not the Same as Higher Consciousness

There is an important distinction to make here.

A more complex biological feature does not necessarily mean a more advanced order of consciousness.

Consider an eagle. Its visual system is extraordinary. In several respects, its eyesight exceeds our own. It can fly, and its body is exquisitely adapted to aerial movement, hunting and navigation. A human cannot compete with an eagle in the sky.

But this does not mean the eagle therefore possesses a higher order of consciousness.

Why?

Because dimensional development is not measured simply by how sophisticated a body part is. It is measured by the range of relationships consciousness can enter into.

The eagle relates magnificently to its ecological world. It navigates vast distances, recognises prey, responds to danger, raises offspring and learns from its environment.

But the human relational world extends into entirely different territories.

We relate not only to what is immediately present, but to things that may never have been physically present before us. We relate to ancient civilisations, distant galaxies, mathematical objects, imagined futures, moral principles, political systems, stories, music, history, atoms we cannot see and universes we cannot visit.

A human being can spend an entire lifetime trying to understand a star that existed billions of years before that person was born.

That is a remarkable kind of relationship.

So greater consciousness should not be confused with greater biological engineering. The eye of an eagle may outperform ours. A whale may navigate oceans we could never survive unaided. A dog may smell realities completely invisible to our senses.

The question is not, Which organism has the most impressive body?

The deeper question is, How far can its relationships extend?

Perhaps consciousness advances not simply by becoming more complex, but by becoming capable of entering into increasingly broad, deep and abstract relationships with reality.

The eagle and the human therefore remain within the same Third Dimension of agency. What differs is not their dimension, but the level of relational development they occupy within it.

📶 Different Levels Within the Same Dimension

A dimension is not a single level of development. It contains many levels within it.

An insect, an animal and a human can all belong to the Third Dimension because they share the fundamental freedom of agency. Yet this does not mean their relational capacities are equal. There may be many levels between them, just as there may also be meaningful differences in relational development between individuals of the same species.

What defines the dimension is the kind of freedom available. What distinguishes the levels within that dimension is the breadth, depth and complexity of the relationships consciousness can enter into.

A new dimension is reached only when a genuinely new category of relational freedom appears — not simply when an existing capacity becomes more advanced.

🪆 Levels Inside Levels

One of the most elegant features of this framework is that the dimensions do not replace one another. They accumulate.

A plant contains matter. A mobile living being contains matter and life. Agency depends upon the living organism, which depends upon the material structure beneath it.

The first dimension does not vanish when the second appears, and the second does not disappear when the third emerges. They remain, continue operating, and become part of something larger.

A human body is therefore not simply a third-dimensional relational structure. It contains all three orders simultaneously: the atoms exist, the cells live and grow, and the organism acts.

Existence. Life. Agency. All nested within one another.

But there is another possibility.

The dimensions may do more than merely sit inside one another.

They may begin to cooperate.

🐝 When Dimensions Begin to Cooperate

Imagine an early world of plant life.

Plants can reproduce in many ways. Wind carries pollen, water carries reproductive material, seeds fall and spores travel. In these relationships, life interacts largely with the physical forces already surrounding it.

The first and second dimensions work together.

Then mobile life enters the picture.

Now something new becomes possible.

A bee visits a flower. The bee seeks food, the flower offers nectar, and pollen travels from one plant to another. The plant benefits from the movement of the bee, while the bee benefits from the resources of the plant.

Neither relationship is simply one-dimensional. A living structure rooted in place enters into a cooperative relationship with a mobile agent. Two different relational capacities begin to interact.

Over evolutionary time, some of these relationships become extraordinarily intimate. Certain plants depend heavily upon particular pollinators, while certain animals depend upon particular plants. Entire ecosystems emerge from networks of interdependence between organisms possessing different kinds of freedom.

The appearance of a higher relational dimension therefore does not make the lower ones obsolete. It can create new possibilities for them.

A plant that cannot move may nevertheless extend its reproductive reach through a creature that can. The bee gains nourishment, while the plant gains mobility indirectly. Something neither could accomplish alone becomes possible through relationship.

This may reveal a deeper principle.

Perhaps increasing complexity in reality is not simply the creation of higher and higher levels. Perhaps it is also the increasing connection between them.

Dimensions remain, but as reality develops, their relationships become richer and their cooperation more intricate.

The universe becomes less like a ladder and more like a web.

🌳 The Same Garden, Different Worlds

Now imagine a plant and a human in the same room.

The human knows the plant exists. We water it, move it, prune it and make sure it receives sunlight. We may even become emotionally attached to it.

But what about the other direction?

When you water the plant, it responds to moisture. When you open the blinds, it responds to light. When you pick it up and carry it across the room, its environment changes dramatically.

But can the plant recognise the intention behind what happened? Can it understand that another conscious being made a decision to help it?

Probably not in anything resembling the way we understand intention.

From its relational position, the event may simply register as a change in conditions: water, light, movement, temperature.

But behind those conditions is something the plant may have no capacity to recognise — a mind making a choice.

The human and the plant occupy the same physical room, but they do not occupy the same relational world.

Human civilisation constantly surrounds plant life. Languages, governments, science, art, history, music, the internet, wars, love stories and space exploration all happen beside trees that may live for hundreds of years.

The tree is physically present for human history.

But human history is not part of the relational world available to the tree.

Not because history is far away, but because the tree does not possess the kind of relational access required to enter into it.

The gap between worlds may not always be distance.

Sometimes it may be capacity.

🌧️ When a Higher Level Just Looks Like the Weather

And this leads somewhere rather strange.

From the plant's point of view, the deliberate actions of a human may appear simply as conditions. Water arrives, light changes, the pot moves, a branch is cut. The plant responds to the effects without necessarily recognising the source.

In that sense, the intentional activity of a higher relational order may appear to the lower order simply as... nature.

Now turn the question upward.

Suppose there were an order of existence above ours — something possessing a relational freedom genuinely unavailable to human beings.

Would we necessarily recognise its actions?

Perhaps not.

Perhaps we would experience only the effects, and because we could not perceive the source, we would give those effects other names: coincidence, luck, synchronicity, natural law, fate, God, the universe, randomness, or simply the way things happen.

This is not proof that higher beings exist or that they interfere in human lives. It is simply a philosophical consequence of the dimensional idea: experiencing an effect does not guarantee that you possess the relational capacity to recognise its source.

The plant may experience the watering.

But not the gardener.

Perhaps that possibility is worth sitting with for a moment.

🌌 Maybe Higher Dimensions Aren't Somewhere Else

When people imagine higher dimensions, they often imagine another place: a parallel universe, a distant realm, something hidden beyond the stars, or something curled into scales too small for us to perceive.

But relational difference does not necessarily require physical separation.

The human and the plant occupy the same room. Their worlds are radically different, not because one is distant from the other, but because each has access to different kinds of relationships.

Why should a higher order of existence necessarily be somewhere else?

If such an order existed, perhaps it could overlap our world completely. Perhaps the separation would not be spatial.

Perhaps it would be relational.

We recognise the plant. The plant responds to our actions without necessarily recognising what we are.

Could something else recognise us in the same way?

We do not know.

But once the question is asked, it becomes surprisingly difficult to dismiss simply by pointing toward the sky and saying, There's nothing there.

Perhaps there was never the right place to look.

🌠 What Comes After Agency?

If the pattern continues, a fourth relational dimension would need to introduce something as genuinely new as life was to simple existence, or as agency was to rooted life.

Not merely greater intelligence, faster thinking, better technology, or a creature that can run faster, see farther or calculate more accurately. Those are improvements within freedoms we already possess.

A genuine higher dimension would introduce a new category of freedom — something we currently lack, and perhaps something we might struggle even to describe.

One possibility is a fundamentally different relationship with time.

Human beings possess remarkable freedom in space. We move forward, backward, left, right, up and down. We travel across continents and beyond our planet.

But time is different.

We remember the past, experience the present and imagine the future. Yet we do not appear able to move freely between them. We are carried through time; we do not navigate it as we navigate space.

What if a higher relational order experienced time differently?

What if what appears to us as an irreversible sequence appeared to something else more like terrain? Not a river carrying the observer forward, but a landscape.

That is speculation, and it should remain speculation.

But the principle is more important than the example.

A genuine higher dimension should introduce a new relational freedom — not merely a more powerful version of a freedom we already possess.

And the difficulty is obvious.

How can a being fully imagine a freedom it does not yet have?

A plant cannot imagine walking.

Perhaps there are things we cannot imagine for exactly the same reason.

🧠 Consciousness All the Way Down

This framework begins from one fundamental philosophical position: consciousness does not suddenly appear after matter becomes complicated enough.

Consciousness is primary.

What changes is not whether consciousness exists, but the range of relationships through which it can express itself.

At the most basic level, consciousness participates through existence and interaction. At richer levels, it participates through living organisation. At still richer levels, through agency. And perhaps beyond those, through forms of relation we do not yet possess.

This means increasing organisation should not be mistaken for the creation of consciousness. Organisation is better understood as one expression of what consciousness becomes capable of coordinating when richer relationships become available.

But again, complexity alone is not the measure.

A single organ can be extraordinarily sophisticated without making the entire being relationally more advanced. The eagle's eye reminds us of that.

The question is not simply how complex the structure becomes.

The question is what the consciousness expressed through that structure can relate to.

A stone, a plant, an insect, an eagle and a human do not represent a journey from completely unconscious matter to suddenly conscious beings. They represent different organisations and expressions of consciousness — different ranges of participation, different relational horizons, different worlds existing inside the same world.

🗼 Picture a Tower

Imagine existence as a tall tower with many floors.

On the first floor, you can be. On the second, you can be and grow. On the third, you can be, grow and act. Each floor contains what came before, but every new floor changes what becomes possible.

Now imagine standing on the third floor and looking downward. You can study the floors below, interact with them, use them, care for them, and perhaps even understand something about the rules by which they operate.

But from the ground floor, looking upward may be impossible.

Not because the upper floors are deliberately hiding, but because the lower floor has no window facing them.

If there are floors above ours, perhaps the same principle applies. Those above may be capable of looking downward, while we may not yet be capable of looking up.

And perhaps the strange mistake is that we spend so much time imagining higher dimensions in distant universes while overlooking the dimensional progression already visible beneath our feet:

The stone → the tree → us.

Maybe the first clue has been sitting in the garden all along.

🔬 What Does Physics Say? — For the Curious

The relational model described here does not depend upon modern physics, but physics has its own remarkable history of thinking about dimensions, and the parallels are worth exploring.

⏳ Relativity — Space Isn't Enough

We naturally experience the world through three spatial dimensions: up and down, left and right, forward and backward.

But describing an event requires more than saying where it happened. You also need to know when.

Imagine arranging to meet someone. You give them the building, the floor and the room, but no time. You have not described a meeting. You have described an empty room.

Relativity and Minkowski's spacetime formulation brought space and time into a unified four-dimensional description of events.

And something even stranger followed.

Time does not pass identically for every observer. Motion affects elapsed time. Gravity affects elapsed time. There is no single universal cosmic clock ticking at exactly the same rate everywhere.

Time is woven into the structure of spacetime itself.

🧩 Kaluza and Klein — A Hidden Fifth Dimension

In 1921, physicist Theodor Kaluza explored what would happen if Einstein's gravitational equations were extended into five dimensions.

Something remarkable appeared. The mathematics contained structures resembling both gravity and electromagnetism.

A few years later, Oskar Klein developed the idea further and proposed that the additional spatial dimension might be compactified — curled up at an extremely small scale.

Imagine a garden hose viewed from far away. From a distance, it appears to be a line. But an ant walking on the hose can move in two directions: along its length or around its circumference.

The second direction was always there.

It simply wasn't obvious from your perspective.

🧵 Superstring Theory — Even More Dimensions

The idea of additional dimensions later became important in superstring theory.

Instead of treating the fundamental ingredients of nature purely as point-like particles, string theories describe tiny one-dimensional objects whose different modes of vibration correspond to different physical states.

Consistent superstring theories are formulated in ten spacetime dimensions.

So where are the additional dimensions?

One possibility is that the extra spatial dimensions are compactified at scales far too small for us to observe directly.

Again, something can be present in reality without being directly accessible to ordinary human perception.

But this raises another philosophical question.

Is physical size the only reason something might remain beyond our perception?

Or could something be inaccessible because our particular kind of existence lacks the relational capacity required to engage with it?

Something may be hidden because it is too small. But perhaps something could also be hidden because it involves a kind of freedom we do not possess.

🌌 M-Theory — Eleven Dimensions

During the 1990s, physicists discovered deep connections between several previously distinct superstring theories.

Edward Witten and others helped develop the idea of a broader eleven-dimensional framework commonly called M-theory. Within this framework appear higher-dimensional objects known as branes — short for membranes.

M-theory remains theoretical. It has not been experimentally confirmed as a description of nature.

But its dimensional structure illustrates something fascinating about human thought.

We began our everyday experience with three spatial dimensions. Modern physics describes four-dimensional spacetime. Kaluza and Klein explored five-dimensional models. Superstring theories involve ten spacetime dimensions, while M-theory involves eleven.

Mathematics itself can describe spaces of many different dimensionalities. Eleven is therefore not some universal mathematical wall around reality; it is a feature of a particular theoretical framework.

And there is one more thing worth considering.

All of these theories were created by human minds — minds operating from within the relational capacities available to human beings.

Our mathematics is extraordinarily powerful.

But if genuinely higher relational orders existed, would they describe reality through mathematics as we understand it?

Perhaps.

Perhaps not.

Perhaps they would possess ways of relating to reality that we could no more understand than a plant could understand a telescope.

That is not an argument against mathematics. Quite the opposite.

It is a reminder of something science itself repeatedly teaches us:

The limits of an observer are not necessarily the limits of reality.

🧭 Two Different Questions That Share a Structure

Physics and the relational model are asking different questions.

Physics asks: How many dimensions are required to describe the mathematical and physical structure of the universe?

The relational model asks: What new degrees of freedom become available to existence as consciousness enters into increasingly rich forms of relationship?

These are not the same question, and they should not be confused.

But there is an intriguing similarity between them.

In both cases, a dimension introduces possibilities unavailable from a more limited frame of reference.

Physics has already taught us to take seriously the possibility that reality may contain structures we cannot directly perceive. The relational question takes that intuition in another direction.

What if dimensional difference can also concern what a being is capable of doing, experiencing, recognising, understanding and relating to?

Perhaps these are simply two completely different uses of the word dimension.

Or perhaps they are distant reflections of some deeper principle.

For now, we don't know.

And perhaps that is exactly what makes the question interesting.

🌟 So — Were the Dimensions Ever Missing?

We began with a simple question:

If we live in the third dimension, where are the first and second?

Perhaps one answer is that they are in the garden, in the stone on your windowsill, in the tree outside your house and in the flower growing beside the road.

The first dimension is there in existence itself. The second appears through life and growth. The third opens through agency.

And the dimensions do not vanish as new ones arise.

They remain, nest, cooperate and form relationships with one another.

The stone supports the soil. The soil supports the plant. The plant feeds the bee. The bee pollinates the plant. The human observes the entire relationship — and then wonders what it means.

Each level participates in a reality larger than itself.

Perhaps that is the deeper pattern.

The dimensions were never empty, never missing and never hidden.

We simply weren't looking at them this way.

The first dimension: Existence.
The second: Life and Growth.
The third: Agency.

And beyond agency?

We do not know.

But perhaps what we call coincidence, synchronicity, nature, fate, or simply the way things are could sometimes represent relationships whose sources we do not yet possess the capacity to recognise.

That is not a claim.

It is a question.

And sometimes a good question does something extraordinary:

It changes where we look.

📚 About This Article

This article explores dimension as a progression of relational freedoms — from existence, to life and growth, to agency, and potentially beyond.

Related topics explored elsewhere on this site include

• Consciousness

• Time

• Frames of Time

• Hierarchical Consciousness

• The Self

• Foundational Definitions.

References

• Einstein, A. (1915). The Field Equations of Gravitation.

• Green, M. B., & Schwarz, J. H. (1984). Anomaly Cancellations in Supersymmetric D = 10 Gauge Theory and Superstring Theory.

• Kaluza, T. (1921). Zum Unitätsproblem der Physik.

• Klein, O. (1926). Quantentheorie und fünfdimensionale Relativitätstheorie.

• Minkowski, H. (1909). Raum und Zeit.

• Townsend, P. K. (1995). The Eleven-Dimensional Supermembrane Revisited.

• Witten, E. (1995). String Theory Dynamics in Various Dimensions.

• Duff, M. J. (1996). M-Theory (the Theory Formerly Known as Strings).

🔎 Similarity Theory Summary:
Similarity Theory is a cosmological framework for understanding consciousness and the universe, discovered through the principle of similarity.
You do not observe consciousness directly—you observe its similarities across frames.

Similarity is epistemological (how we detect and understand).
Consciousness is ontological (what actually exists).

Unity is temporary; individuality is eternal.

Despite its name, Similarity Theory is not a theory about similarity itself, but a framework for understanding consciousness, time, and the structure of reality. Similarity is the method through which these structures are discovered and observed.
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